A full Bayesian multilevel approach for modeling interaction effects in single-vehicle crashes

Interaction effects constitute crucial crash attributes that can be classified into two distinct categories: spatiotemporal interactions and factor interactions. These interactions are rarely addressed systematically in modeling the severity of single-vehicle (SV) crashes. This study focuses on uncovering these crash attributes by designing a full Bayesian spatiotemporal interaction multilevel logit (STIML-logit) approach with heterogeneity in means and variances (HMV). Meanwhile, a nested Gaussian conditional autoregressive (CAR) structure is proposed to fit the spatiotemporal interaction component and its effectiveness is verified by calibrating four different interaction patterns. A standard multilevel logit (with and without HMV), a multilevel logit with HMV, and a spatiotemporal multilevel logit with HMV are constructed for comparison. Risk factors are decomposed into traffic environment factors (group level) and individual crash factors (case level) to construct a multilevel structure and to capture possible interactions between risk factors from different levels (cross-level factor interactions). We perform regression modeling utilizing SV crash cases covering 96 major urban roads in Shandong, China. The modeling results underscore several significant findings: (1) the STIML-logit with HMV demonstrates the best regression performance, suggesting that systematically dealing with the interaction effects and the HMV is a trustworthy modeling perspective; (2) crash models with the nested CAR outperform those with the traditional CAR and the result is supported by all the spatiotemporal statistical functions, highlighting the potential advantages of the nested structure; (3) all the environment factors maintain significant interactions with the case factors, highlighting that the contribution of the environment factors to crash injuries is not constant but is rather influenced by the specific case-related crash factors. The study introduces a promising regression architecture for modeling crash injuries and revealing subtle crash attributes.